Question: $ {10\cdot \left[ \begin{array}{cc} 1 & 2 \\ 1 & 0 \\ 4 & -2 \end{array} \right]=}$
Solution: The Strategy To multiply a matrix by a scalar, we multiply each term of the matrix by the scalar. Multiplying each term $ {\begin{aligned}10\cdot \left[\begin{array}{rr} {1} & {2} \\ {1} & {0} \\ {4} & {-2} \end{array}\right]&=\left[\begin{array}{rr} 10\cdot{1} & 10\cdot{2} \\ 10\cdot{1} & 10\cdot{0} \\ 10\cdot{4} & 10\cdot{-2} \end{array}\right] \\\\&=\left[\begin{array}{rr} {10} & {20} \\ {10} & {0} \\ {40} & {-20}\end{array}\right]\end{aligned}}$ Summary $ {10\cdot \left[ \begin{array}{cc} 1 & 2 \\ 1 & 0 \\ 4 & -2 \end{array} \right]=\left[ \begin{array}{cc} 10 & 20 \\ 10 & 0 \\ 40 & -20 \end{array} \right]}$